Question: Simplify the following expression and state the condition under which the simplification is valid: $y = \dfrac{a^2 - 5a}{a^2 + 4a - 45}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{a^2 - 5a}{a^2 + 4a - 45} = \dfrac{(a)(a - 5)}{(a + 9)(a - 5)} $ Notice that the term $(a - 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(a - 5)$ gives: $y = \dfrac{a}{a + 9}$ Since we divided by $(a - 5)$, $a \neq 5$. $y = \dfrac{a}{a + 9}; \space a \neq 5$